Hahah, I totally see your point but lion prides actually are kind of like matriarchal feminist republics. They don't do that misandry thing people are so fond of, though.

Lion society is actually composed of the two discrete units of male coalitions and females and cubs (with subadults being another sub-unit). Males with tenure will spend time with their harems of females (and a coalition will have up to two or even three if the land is thick), but among male lions the coalition is the basic unit.

Lionesses can and will run off male lions violently, especially if there's only one. And it's almost unheard of for a single male lion to hold onto his tenure in a pride for any significant length of time - it doesn't take long for another coalition (of 2-5 males) to run him off the land.

As for hunting, while it's true that lions on the serengeti plains tend to display a level of sexual role assignment (mostly, as George Schaller found out in his seminal Serengeti Lion studies, because they have big manes that are obvious on open plains). In other parts of Africa where lions are less-studied, such as the veldt and the desert where there's more cover and/or males have smaller manes or none at all, both sexes take part in hunting. And anyway, male lions coalitions must make do with finding their own food (typically by scavenging, often, ironically, from hyenas, who are better hunters in reality) when they're not spending time with a female pride and/or when they're in limbo between tenure with a pride.

It's also worth mentioning that while infanticide is very common because, obviously, no male lion wants to expend resources and energy looking after another guy's kids. While many lionesses appear unbothered by this, it's just as common for lionesses fight savagely for their cubs or to hide their young, or for younger lions to form straggly bands of subadults that exist on the periphery of a pride, staying out of reach of the adult males.